Statistical Analysis Service

Statistics offers a toolkit of methods for analyzing data—each designed for different research questions and data characteristics. The challenge is knowing which tool to use when. Should you use a t-test or Mann-Whitney U? Regression or ANCOVA? Factor analysis or principal components analysis? Choosing the right method matters because the wrong choice yields incorrect conclusions or misses patterns in your data. Statistical analysis service helps you understand what each method does, when it's appropriate, what assumptions it requires, and how to interpret results. This guide provides an overview of common statistical methods, organizing them by research question type, and explaining the logic behind method selection. Think of it as a statistical decision tree—follow the branches to find the right approach for your research.

Choosing your analytical approach

Step 1: Define your research question

What are you trying to learn from your data?

• Describing a group: "What are the characteristics of our sample?" (Descriptive statistics)
• Comparing groups: "Do groups differ on this variable?" (t-test, ANOVA, chi-square)
• Relationships between variables: "Are two variables related?" (Correlation, regression)
• Predicting an outcome: "Can we predict Y from X?" (Regression, logistic regression)
• Identifying patterns/groups: "What natural clusters exist in the data?" (Cluster analysis, factor analysis)
• Changing over time: "How do scores change across time points?" (Repeated measures ANOVA, mixed models)

Step 2: Identify your variables

What type of data do you have?

• Continuous: Test scores (0–100), age (years), depression severity (0–60 scale). Use parametric tests (t-test, ANOVA, Pearson correlation)
• Ordinal: Likert responses (1–5), ranked items. Use non-parametric tests (Mann-Whitney U, Spearman rho) or treat as continuous if composite scores
• Categorical: Gender, treatment group, pass/fail. Use chi-square, logistic regression

Step 3: Check assumptions

Parametric tests assume normality, homogeneity of variance, independence. If assumptions violated, use non-parametric alternatives or transform data

Common analysis methods by question type

Comparing two groups

• Independent groups, continuous outcome: Independent samples t-test (assume normality/equal variances) or Mann-Whitney U (non-parametric alternative)
• Paired/repeated measures: Paired t-test or Wilcoxon signed-rank test
• Categorical outcome: Chi-square test

Comparing 3+ groups

• Continuous outcome, one factor: One-way ANOVA (if normal/equal variances) or Kruskal-Wallis (non-parametric)
• Multiple factors: Factorial ANOVA (e.g., gender × treatment condition)
• Repeated measures across time: Repeated measures ANOVA or mixed models
• Categorical outcome: Chi-square or logistic regression

Relationships/associations

• Two continuous variables: Pearson correlation (parametric) or Spearman rho (ordinal)
• Predicting continuous outcome: Linear regression (one predictor) or multiple regression (several)
• Predicting binary outcome: Logistic regression
• Two categorical variables: Chi-square test

Advanced/multivariate

• Controlling for confounds: ANCOVA (continuous covariate), multiple regression (multiple predictors)
• Multiple outcome variables simultaneously: MANOVA (multivariate ANOVA)
• Complex designs: Mixed models (handles repeated measures + between-groups factors)
• Identifying latent patterns: Factor analysis (reduces variables to underlying factors), cluster analysis (groups cases)
• Structural relationships: Structural equation modeling (SEM) for complex theoretical models

Parametric vs. non-parametric

Power analysis and sample size

• Power analysis determines: How large a sample do you need to detect an effect if it exists?
• Factors affecting power: Effect size (smaller effects need larger N), significance level (typically α = .05), desired power (typically .80)
• Rule of thumb: Most social science research needs 20–30 per group minimum; larger is always better
• Tools: G*Power software calculates required N before data collection. Consult power analysis EARLY in your design

Data screening before analysis

• Descriptive statistics: Means, SDs, ranges. Do values make sense?
• Outliers: Values far from the group mean. Extreme outliers violate assumptions and should be examined (data entry error? real but unusual case?)
• Missing data: How much is missing? Pattern? MCAR (missing completely at random), MAR (missing at random), MNAR (missing not at random) have different implications
• Normality: Q-Q plots, Shapiro-Wilk test. Slightly non-normal usually okay (parametric tests robust); severely non-normal needs alternatives
• Homogeneity of variance: Levene's test. If unequal variances, use Welch's t-test instead of standard t-test